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arXiv · 2102.12861

New Gaussian Riesz transforms on variable Lebesgue spaces

Estefanía Dalmasso·Roberto Scotto
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Abstract

We give sufficient conditions on the exponent $p: \mathbb R^d\rightarrow [1,\infty)$ for the boundedness of the non-centered Gaussian maximal function on variable Lebesgue spaces $L^{p(\cdot)}(\mathbb R^d, \gamma_d)$, as well as of the new higher order Riesz transforms associated with the Ornstein-Uhlenbeck semigroup, which are the natural extensions of the supplementary first order Gaussian Riesz transforms defined by A. Nowak and K. Stempak in \cite{nowakstempak}.

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Estefanía Dalmasso, Roberto Scotto. 2021-02-25. New Gaussian Riesz transforms on variable Lebesgue spaces. https://doi.org/10.1007/s10476-022-0117-y

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